This paper considers the spectrum sharing network consisting of a pair of primary users (PUs) and a pair of cognitive users (CRs) in a fading channel. The pair of PUs establishes a wireless link as the PU link. The pair of CRs establishes a wireless link as the CR link. The PU link and CR link utilize spectrum simultaneously with different priorities. The PU link has a higher priority to utilize spectrum with respect to the CR link. When the PU link utilizes spectrum, a desired quality of service (QoS) is given to be assured and the CR utilizes spectrum with an opportunistic power scale under this constraint, assuring the desired QoS on the PU link. To compute an optimal opportunistic power scale for the CR link, a fuzzy-based opportunistic power control strategy is proposed based on the Mamdani fuzzy control model using two input variables: the PU’s SNR and PU’s interference channel gain. By the proposed fuzzy-based power control strategy, the desired QoS could be assured on the PU link and the bit error rate (BER) is also reduced compared with the spectrum sharing network without power control strategy.